{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This notebook was prepared by [Donne Martin](https://github.com/donnemartin). Source and license info is on [GitHub](https://github.com/donnemartin/interactive-coding-challenges)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Solution Notebook"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Problem: Implement a trie with find, insert, remove, and list_words methods.\n",
    "\n",
    "* [Constraints](#Constraints)\n",
    "* [Test Cases](#Test-Cases)\n",
    "* [Algorithm](#Algorithm)\n",
    "* [Code](#Code)\n",
    "* [Unit Test](#Unit-Test)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Constraints\n",
    "\n",
    "* Can we assume we are working with strings?\n",
    "    * Yes\n",
    "* Are the strings in ASCII?\n",
    "    * Yes\n",
    "* Should `find` only match exact words with a terminating character?\n",
    "    * Yes\n",
    "* Should `list_words` only return words with a terminating character?\n",
    "    * Yes\n",
    "* Can we assume this fits memory?\n",
    "    * Yes"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Test Cases\n",
    "\n",
    "<pre>\n",
    "\n",
    "root node is denoted by ''\n",
    "\n",
    "         ''\n",
    "       /  |  \\\n",
    "      h   a*  m\n",
    "     / \\   \\   \\\n",
    "    a   e*  t*  e*\n",
    "   / \\         / \\\n",
    "  s*  t*      n*  t*\n",
    "             /\n",
    "            s*\n",
    "\n",
    "find\n",
    "\n",
    "* Find on an empty trie\n",
    "* Find non-matching\n",
    "* Find matching\n",
    "\n",
    "insert\n",
    "\n",
    "* Insert on empty trie\n",
    "* Insert to make a leaf terminator char\n",
    "* Insert to extend an existing terminator char\n",
    "\n",
    "remove\n",
    "\n",
    "* Remove me\n",
    "* Remove mens\n",
    "* Remove a\n",
    "* Remove has\n",
    "\n",
    "list_words\n",
    "\n",
    "* List empty\n",
    "* List general case\n",
    "</pre>\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Algorithm\n",
    "\n",
    "### find\n",
    "\n",
    "* Set node to the root\n",
    "* For each char in the input word\n",
    "    * Check the current node's children to see if it contains the char\n",
    "        * If a child has the char, set node to the child\n",
    "        * Else, return None\n",
    "* Return the last child node if it has a terminator, else None\n",
    "\n",
    "Complexity:\n",
    "* Time: O(m), where m is the length of the word\n",
    "* Space: O(h) for the recursion depth (tree height), or O(1) if using an iterative approach\n",
    "\n",
    "### insert\n",
    "\n",
    "* set node to the root\n",
    "* For each char in the input word\n",
    "    * Check the current node's children to see if it contains the char\n",
    "        * If a child has the char, set node to the child\n",
    "        * Else, insert a new node with the char\n",
    "            * Update children and parents\n",
    "* Set the last node as a terminating node\n",
    "\n",
    "Complexity:\n",
    "* Time: O(m), where m is the length of the word\n",
    "* Space: O(h) for the recursion depth (tree height), or O(1) if using an iterative approach\n",
    "\n",
    "### remove\n",
    "\n",
    "* Determine the matching terminating node by calling the find method\n",
    "* If the matching node has children, remove the terminator to prevent orphaning its children\n",
    "* Set the parent node to the matching node's parent\n",
    "* We'll be looping up the parent chain to propagate the delete\n",
    "* While the parent is valid\n",
    "    * If the node has children\n",
    "        * Return to prevent orphaning its remaining children\n",
    "    * If the node is a terminating node and it isn't the original matching node from the find call\n",
    "        * Return to prevent deleting this additional valid word\n",
    "    * Remove the parent node's child entry matching the node\n",
    "    * Set the node to the parent\n",
    "    * Set the parent to the parent's parent\n",
    "\n",
    "Complexity:\n",
    "* Time: O(m+h), where where m is the length of the word and h is the tree height\n",
    "* Space: O(h) for the recursion depth (tree height), or O(1) if using an iterative approach\n",
    "\n",
    "### list_words\n",
    "\n",
    "* Do a pre-order traversal, passing down the current word\n",
    "    * When you reach a terminating node, add it to the list of results\n",
    "\n",
    "Complexity:\n",
    "* Time: O(n)\n",
    "* Space: O(h) for the recursion depth (tree height), or O(1) if using an iterative approach"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Code"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overwriting trie.py\n"
     ]
    }
   ],
   "source": [
    "%%writefile trie.py\n",
    "from collections import OrderedDict\n",
    "\n",
    "\n",
    "class Node(object):\n",
    "\n",
    "    def __init__(self, key, parent=None, terminates=False):\n",
    "        self.key = key\n",
    "        self.terminates = False\n",
    "        self.parent = parent\n",
    "        self.children = {}\n",
    "\n",
    "\n",
    "class Trie(object):\n",
    "\n",
    "    def __init__(self):\n",
    "        self.root = Node('')\n",
    "\n",
    "    def find(self, word):\n",
    "        if word is None:\n",
    "            raise TypeError('word cannot be None')\n",
    "        node = self.root\n",
    "        for char in word:\n",
    "            if char in node.children:\n",
    "                node = node.children[char]\n",
    "            else:\n",
    "                return None\n",
    "        return node if node.terminates else None\n",
    "\n",
    "    def insert(self, word):\n",
    "        if word is None:\n",
    "            raise TypeError('word cannot be None')\n",
    "        node = self.root\n",
    "        parent = None\n",
    "        for char in word:\n",
    "            if char in node.children:\n",
    "                node = node.children[char]\n",
    "            else:\n",
    "                node.children[char] = Node(char, parent=node)\n",
    "                node = node.children[char]\n",
    "        node.terminates = True\n",
    "\n",
    "    def remove(self, word):\n",
    "        if word is None:\n",
    "            raise TypeError('word cannot be None')\n",
    "        node = self.find(word)\n",
    "        if node is None:\n",
    "            raise KeyError('word does not exist')\n",
    "        node.terminates = False\n",
    "        parent = node.parent\n",
    "        while parent is not None:\n",
    "            # As we are propagating the delete up the \n",
    "            # parents, if this node has children, stop\n",
    "            # here to prevent orphaning its children.\n",
    "            # Or\n",
    "            # if this node is a terminating node that is\n",
    "            # not the terminating node of the input word, \n",
    "            # stop to prevent removing the associated word.\n",
    "            if node.children or node.terminates:\n",
    "                return\n",
    "            del parent.children[node.key]\n",
    "            node = parent\n",
    "            parent = parent.parent\n",
    "\n",
    "    def list_words(self):\n",
    "        result = []\n",
    "        curr_word = ''\n",
    "        self._list_words(self.root, curr_word, result)\n",
    "        return result\n",
    "\n",
    "    def _list_words(self, node, curr_word, result):\n",
    "        if node is None:\n",
    "            return\n",
    "        for key, child in node.children.items():\n",
    "            if child.terminates:\n",
    "                result.append(curr_word + key)\n",
    "            self._list_words(child, curr_word + key, result)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "%run trie.py"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Unit Test"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Overwriting test_trie.py\n"
     ]
    }
   ],
   "source": [
    "%%writefile test_trie.py\n",
    "from nose.tools import assert_true\n",
    "from nose.tools import raises\n",
    "\n",
    "\n",
    "class TestTrie(object):       \n",
    "\n",
    "    def test_trie(self):\n",
    "        trie = Trie()\n",
    "\n",
    "        print('Test: Insert')\n",
    "        words = ['a', 'at', 'has', 'hat', 'he',\n",
    "                 'me', 'men', 'mens', 'met']\n",
    "        for word in words:\n",
    "            trie.insert(word)\n",
    "        for word in trie.list_words():\n",
    "            assert_true(trie.find(word) is not None)\n",
    "            \n",
    "        print('Test: Remove me')\n",
    "        trie.remove('me')\n",
    "        words_removed = ['me']\n",
    "        words = ['a', 'at', 'has', 'hat', 'he',\n",
    "                 'men', 'mens', 'met']\n",
    "        for word in words:\n",
    "            assert_true(trie.find(word) is not None)\n",
    "        for word in words_removed:\n",
    "            assert_true(trie.find(word) is None)\n",
    "\n",
    "        print('Test: Remove mens')\n",
    "        trie.remove('mens')\n",
    "        words_removed = ['me', 'mens']\n",
    "        words = ['a', 'at', 'has', 'hat', 'he',\n",
    "                 'men', 'met']\n",
    "        for word in words:\n",
    "            assert_true(trie.find(word) is not None)\n",
    "        for word in words_removed:\n",
    "            assert_true(trie.find(word) is None)\n",
    "\n",
    "        print('Test: Remove a')\n",
    "        trie.remove('a')\n",
    "        words_removed = ['a', 'me', 'mens']\n",
    "        words = ['at', 'has', 'hat', 'he',\n",
    "                 'men', 'met']\n",
    "        for word in words:\n",
    "            assert_true(trie.find(word) is not None)\n",
    "        for word in words_removed:\n",
    "            assert_true(trie.find(word) is None)\n",
    "\n",
    "        print('Test: Remove has')\n",
    "        trie.remove('has')\n",
    "        words_removed = ['a', 'has', 'me', 'mens']\n",
    "        words = ['at', 'hat', 'he',\n",
    "                 'men', 'met']\n",
    "        for word in words:\n",
    "            assert_true(trie.find(word) is not None)\n",
    "        for word in words_removed:\n",
    "            assert_true(trie.find(word) is None)\n",
    "\n",
    "        print('Success: test_trie')\n",
    "\n",
    "    @raises(Exception)\n",
    "    def test_trie_remove_invalid(self):\n",
    "        print('Test: Remove from empty trie')\n",
    "        trie = Trie()\n",
    "        assert_true(trie.remove('foo') is None) \n",
    "\n",
    "\n",
    "def main():\n",
    "    test = TestTrie()\n",
    "    test.test_trie()\n",
    "    test.test_trie_remove_invalid()\n",
    "\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    main()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Test: Insert\n",
      "Test: Remove me\n",
      "Test: Remove mens\n",
      "Test: Remove a\n",
      "Test: Remove has\n",
      "Success: test_trie\n",
      "Test: Remove from empty trie\n"
     ]
    }
   ],
   "source": [
    "%run -i test_trie.py"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.4.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
